Which Choice Effectively Increases Tunneling Current?

[tkm2002]

Homework Statement

Suppose a tunneling current in an electronic device goes through a potential-energy barrier. The tunneling current is small because the width of the barrier is large and the barrier is high. To increase the current most effectively, what should you do?
a. Reduce the width of the barrier.
b. Reduce the height of the barrier.
c. Either choice (1) or choice (2) is equally effective.
d. Neither choice (1) nor choice (2) increases the current

Homework Equations

The Attempt at a Solution

should I use this equation?
T ≈ e^(-2CL) , L is he width of the barrier.
c^2 = 2m(U-E)/(h/2pi) , U is the height of the barrier ; E is the energy of electron ;m is the mass of electro; h is plank constant

I am not understand why the answer is a.

 

[gabbagabbahey]

should I use this equation?
T ≈ e^(-2CL) , L is he width of the barrier.
c^2 = 2m(U-E)/(h/2pi) , U is the height of the barrier ; E is the energy of electron ;m is the mass of electro; h is plank constant

I am not understand why the answer is a.

Yes, use those equations. What happens if you cut 'U' in half? What happens if you cut 'L' in half?...So which has the greater effect?

 

[tkm2002]

Yes, use those equations. What happens if you cut 'U' in half? What happens if you cut 'L' in half?...So which has the greater effect?

I do not know how to calculate and compare it

 

[gabbagabbahey]

Call the initial U, [itex]U_0[/itex] and the initial L, [itex]L_0[/itex]...what does that make the initial transmission coefficient? What doe the transmission coefficient become when you plug in [itex]U=U_0/2[/itex] and [itex]L=L_0[/itex]? How about when you plug in [itex]U=U_0[/itex] and [itex]L=L_0/2[/itex]

 

[tkm2002]

Call the initial U, [itex]U_0[/itex] and the initial L, [itex]L_0[/itex]...what does that make the initial transmission coefficient? What doe the transmission coefficient become when you plug in [itex]U=U_0/2[/itex] and [itex]L=L_0[/itex]? How about when you plug in [itex]U=U_0[/itex] and [itex]L=L_0/2[/itex]

But I do not how to compare them
http://img98.imageshack.us/img98/6779/89062472.jpg

[itex]T_0[/itex] = e^2CL
[itex]T of L_0/2[/itex] = [itex]T_0[/itex]^1/2
I do not how to write [itex]T of U_0/2[/itex] in terms of [itex]T_0[/itex]

 

[gabbagabbahey]

Well, the largest effect that the first one will have is to reduce the exponent by a factor of [itex]\sqrt{2}[/itex] (when E=0)...While the second one reduces the exponent by a factor of 2...

P.S. You are missing the negative signs in your exponents!

 

[tkm2002]

Well, the largest effect that the first one will have is to reduce the exponent by a factor of [itex]\sqrt{2}[/itex] (when E=0)...While the second one reduces the exponent by a factor of 2...

P.S. You are missing the negative signs in your exponents!

I am not very understand.
Can you express the equation?